"LG Display is launching a new era of flexible displays for smartphones with its industry-leading technology," Dr. Sang Deog Yeo, Executive Vice President and Chief Technology Officer of LG Display, said in a press release. "The flexible display market is expected to grow quickly as this technology is expected to expand further into diverse applications including automotive displays, tablets and wearable devices."

"Our goal is to take an early lead in the flexible display market by introducing new products with enhanced performance and differentiated designs next year," Yeo added.

The new device comes a few months after LG and Samsung introduced their 55-inch curved television screens, which has a thin, bendable layer of organic light-emitting diodes, The Associated Press reported. The curved television screens will be sold for $15,000 each.

LG did not reveal whether the curved screens on the phones will be flexible.Forbes magazine predicted that the screens will likely be fixed, considering the six-inch displays only flex from top to bottom.

In contrast, Samsung's screens curve side to side, a source with knowledge of the matter told Reuters.

Both companies have reportedly floated the idea of having curved mobile devices for years, but manufacturing challenges and concerns over how customers would react stopped them from developing a model, Forbes noted.

In January, Samsung unveiled a prototype phone that had a flexible screen and curves on the two long sides, TheVerge.com reported.